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If \(x\) is a positive integer, is \(x\) a prime number?
(1) \(x\) is a multiple of a prime number.
(2) \(x=a*b\), where \(a\) and \(b\) are different integers.
Official Solution:If \(x\) is a positive integer, then is \(x\) a prime number? (1) \(x\) is a multiple of a prime number. If \(x=2\) then the answer is Yes (recall that an integer is a multiped of itself) but if \(x=4\) then the answer is NO. Not sufficient.
(2) \(x=a*b\), where \(a\) and \(b\) are different integers. Any integer greater than 1
can be represented as the product of two different integers. For example, \(x=2=prime=1*2=2\) or \(x=4=not \ prime =1*4\). Not sufficient.
(1)+(2) From (2) we only get that \(x\) is not 1, which does not help us to determine whether \(x\) is prime. For example, if \(x=2\) then the answer is Yes but if \(x=4\) then the answer is NO. Not sufficient.
Answer: E